Is Uniqueness Their Common and Only Correct Answer?
I. We often say that xx has no physical meaning or has physical meaning. So what is "physical meaning" and what is the meaning of "physical meaning "*?
"As far as the causality principle is concerned, if the physical quantities and their time derivatives are known in the present in any given coordinate system, then a statement will only have physical meaning if it is invariant with respect to those transformations for which the coordinates used are precisely those for which the known present values remain invariant. I claim that all assertions of this kind are uniquely determined for the future as well, i.e., that the causality principle is valid in the following formulation: From knowledge of the fourteen potentials ......, in the present all statements about them in the future follow necessarily and uniquely insofar as they have physical meaning" [1].“Hilbert's answer is based on a more precise formulation of the concept of causality that hinges on the distinction between meaningful and meaningless statements.”[2]
Hawking said [4], "I take the positivist view that a physical theory is nothing more than a mathematical model, and it is pointless to ask whether it corresponds to the real. All one can seek is that its predictions agree with its observations."
Is there no difference between physics and Mathematics? We believe that the difference between physics and mathematics lies in the fact that physics must have a physical meaning, whereas mathematics does not have to. Mathematics can be said to have a physical meaning only if it finds a corresponding expression in physics.
II. We often say, restore naturalness, preserve naturalness, the degree of unnaturalness, Higgs naturalness problem, structural naturalness, etc., so what is naturalness or unnaturalness?
“There are two fundamental concepts that enter the formulation of the naturalness criterion: symmetry and effective theories. Both concepts have played a pivotal role in the reductionist approach that has successfully led to the understanding of fundamental forces through the Standard Model. ” [6]
Judging naturalness by symmetry is a good piece of criteria; symmetry is the only result of choosing stability, and there seems to be nothing lacking. But using effective theories as another criterion must be incomplete, because truncate obscures some of the most important details.
III. We often say that "The greatest truths are the simplest"（大道至简†）, so is there a standard for judging the simplest?
"Einstein was firmly convinced that all forces must have an ultimate unified description and he even speculated on the uniqueness of this fundamental theory, whose parameters are fixed in the only possible consistent way, with no deformations allowed: 'What really interests me is whether God had any choice in the creation of the world; that is, whether the necessity of logical simplicity leaves any freedom at all' ”[6]
When God created the world, there would not have been another option. The absolute matching of the physical world with the mathematical world has shown that as long as mathematics is unique, physics must be equally unique. The physical world can only be an automatic emulator of the mathematical world, similar to a Cellular Automata.
It is clear that consensus is still a distant goal, and there will be no agreement on any of the following issues at this time:
1) Should there be a precise and uniform definition of having physical meaning? Does the absence of physical meaning mean that there is no corresponding physical reality?
2) Are all concepts in modern physics physically meaningful? For example, probabilistic interpretation of wave functions, superposition states, negative energy seas, spacetime singularities, finite and unbounded, and so on.
3) "Is naturalness a good guiding principle?"[3] "Does nature respect the naturalness criterion?"[6]
4) In physics, is simplicity in essence uniqueness? Is uniqueness a necessary sign of correctness‡?
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Notes：
* xx wrote a book, "The Meaning of Meaning", which Wittgenstein rated poorly, but Russell thought otherwise and gave it a positive review instead. Wittgenstein thought Russell was trying to help sell the author and Russell was no longer serious [5]. If one can write about the Meaning of Meaning, then one can follow with the Meaning of Meaning of Meaning. In that case, how does one end up with meaning? It is the same as causality; there must exist an ultimate meaning which cannot be pursued any further.
‡ For example, the Shortest Path Principle, Einstein's field equation Gµν=k*Tµν, all embody the idea that uniqueness is correctness (excluding the ultimate interpretation of space-time).
† “万物之始，大道至简，衍化至繁。”At the beginning of all things, the Tao is simple; later on, it evolves into prosperous and complexity. Similar to Leonardo Da Vinci，＂Simplicity is the ultimate sophistication.＂ However, the provenance of many of the quotes is dubious.
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References：
[1] Rowe, D. E. (2019). Emmy Noether on energy conservation in general relativity. arXiv preprint arXiv:1912.03269.
[2] Sauer, T., & Majer, U. (2009). David Hilbert's Lectures on the Foundations of Physics 1915-1927: Relativity, Quantum Theory and Epistemology. Springer.
[3] Giudice, G. F. (2013). Naturalness after LHC8. arXiv preprint arXiv:1307.7879.
[4] Hawking, S., & Penrose, R. (2018). The nature of space and time (吴忠超，杜欣欣, Trans.; Chinese ed., Vol. 3). Princeton University Press.
[5] Monk, R. (1990). Ludwig Wittgenstein: the duty of genius. London: J. Cape. Morgan, G. (Chinese @2011)
[6] Giudice, G. F. (2008). Naturally speaking: the naturalness criterion and physics at the LHC. Perspectives on LHC physics, 155-178.
The definition of ``physical meaning'' is `ìnvariance under the transformations that leave the mathematical description of the natural phenomenon of interest invariant''.
When we seek new knowledge about the physical world around us, our first thoughts are intuitive in nature, they are based on the analysis of new and already known facts, as well as on the search for connections between them. Together with consciousness, the subconscious, which is poorly controlled by us, is also used, while no mathematical models are used except analogies with already known phenomena and the models used there. And only then a new mathematical model is synthesized, which approximately describes the intuitive idea that emerged as a result of generalization of experimental facts.
Therefore, the physical meaning is always intuition, supported by a mathematical model. Which, in turn, will always remain a rigid scheme based on logic. But a physical representation, unlike mathematical models, will always be incomplete and capable of changing the very foundations on which the models were based.
With best regards,
Mikhail Dulin.
Dear Mr. Chian Fan ,
Your profound exploration into the intricate relationship between mathematics and physics, as well as your contemplation on the nature of physical meaning and the implications of the Planck scale, offers a rich tapestry of insights into the complexities of these disciplines. Building upon your astute observations, let's delve deeper into the intricate interplay between mathematics, physics, and sensory perception.
Mathematics, as you eloquently described, serves as both an abstract science and a practical tool, encompassing a vast array of topics from number theory to geometry. It provides physicists with the language and tools necessary to formulate and solve complex problems, as exemplified by Newton's invention of calculus to describe motion. Conversely, physics serves as a wellspring of inspiration for mathematicians, with theoretical concepts such as general relativity and quantum theory catalysing the development of new mathematical frameworks.
Your elucidation on physical meaning resonates deeply with the fundamental tenets of scientific inquiry. Physical meaning, rooted in material existence and perceptible through the senses, underpins our understanding of the natural world. The sensory system, with its intricate mechanisms for processing and interpreting information, shapes our perception of the environment and influences our interactions with it. This intimate relationship between sensory perception and the physical world underscores the profound role of human cognition in shaping our understanding of reality.
Furthermore, your exploration of the Planck scale adds another dimension to our discussion. The Planck scale, with its fundamental limits and theoretical implications, challenges our conventional notions of sensory perception and empirical observation. While beyond the realm of direct sensory experience, Planck units derived from fundamental constants provide a theoretical framework for exploring the universe at extreme scales. They underscore the potential limitations of our current scientific models and serve as a reminder of the boundless mysteries that lie beyond our immediate grasp.
In contemplating the Planck scale, we are confronted with the profound interplay between theoretical constructs and empirical reality. While not directly perceptible through sensory experience, concepts such as the Planck length and Planck time hold immense significance within the framework of theoretical physics. They symbolize the frontiers of human knowledge and the ongoing quest to unravel the mysteries of the cosmos.
Your insights into the Planck scale, physical meaning, and the relationship between mathematics and physics illuminate the intricate tapestry of human understanding. They invite us to ponder the nature of reality, the limits of perception, and the boundless potential of scientific inquiry. As we navigate the complexities of the universe, your reflections serve as beacons guiding us toward a deeper understanding of the world around us.
Additionally, I would like to refer you to a relevant and meaningful paper titled Technical Report The Human Brain, Mind, and Consciousness: Unveiling the Enigma
(DOI: 10.13140/RG.2.2.29992.14082). This paper delves into the enigmatic realms of human consciousness and cognition, offering profound insights into the workings of the human brain and mind. It provides valuable perspectives on the intricate relationship between mathemetics, physical perception, neuroscience, psychology, and philosophy, further enriching our understanding of the complexities of the human experience.Best regards,
Soumendra Nath Thakur
Dear Soumendra Nath Thakur
Thank you for your interest and comments, but your kind words have embarrassed me. I cannot bear such an honor. They belong to the physicists of Planck's time.
Planck scales are an important line of research in physics today. It is always good to have this discussion brought to the forefront.
I will read your paper, which deals with a subject that concerns all of us. They are the ultimate scientific research goals that embody the power of the human mind.
Best Regards, Chian Fan
What is Physical meaning, Naturalness and Simplicity?
My response is how to construct all the Universe only from begining with universal constants: From Nothing you get the theory of Everything.
Alaya Kouki With respect to „From Nothing you get the theory of Everything.„ well not from nothing (exactly in the human sense of this word) …
… but from simple first order multiplicative base entities like shown within the framework of iSpace theory able to derive value and geometry of constants of nature, that is (e.g only) GoldenRatio iSpaceAmpere being the quantum of Ampere, 1/6961 iSpaceSecond being the quantum of time, and so on) all multiplied up by any arbitrary positive integer to the values we see once lossless (keeping initial integer geometric exactness!) converted back to iSpace-SI based MKS/A-SI lab compatible measurement values (to compare to experimental results of all kind, given no other theoretical corrections have been applied like QCD/QED when involved in such calculation).
But otherwise - indeed - from nothing (but a little bit pre-school multiplicative math).
Based on my findings i would answer the question
"Is there no difference between physics and Mathematics? We believe that the difference between physics and mathematics lies in the fact that physics must have a physical meaning, whereas mathematics does not have to. Mathematics can be said to have a physical meaning only if it finds a corresponding expression in physics."
Like this:
in Mathematics, 11 = (-1)2 =13
in Physics L1 is not (-L)2 is not L3
Therefore physics must set the rules how numbers are to be used.
Looking at history, it seems to me that it happened around 1834 that the Avogadro constant was introduced into physics as a purely arbitrary number as part of the study of electricity. The ampere was then defined using chemical processes in the German Empire in 1898 through electrolysis and was thus introduced into physics as an arbitrary number. This situation was finally cemented and sealed with the final definition of the ampere in 1948. Now physics seems hopelessly lost to me because this process cannot simply be reversed, but today's physics is actually no longer physics, but actually just mathematics with no meaningful meaning.
Preprint What is Space Time? A clear solution to Einsteins puzzle.
Poster Proposals for standardizing the formulation of natural laws ...
Essential is to understand that
E=mc^2
is
Surface = pi r^2
-> Physics is not physics anymore but confused mathematics.
Dear @all
Everyone's opinion is valuable.
My personal view is that the high degree of consistency between physics and math shows that physics is the natural form of expression of math. There are no exceptions and there will be no exceptions.
Conceptually, physics is a subset of mathematics.
In reality, physical reality is an auto-evolutionary simulator of mathematics that is precise and free of any confusion; it is not physical reality that is confused, but physical science.
In methodology, physical reality must have the basic quantities of mathematics and the relations of motion between the basic quantities. Then the order of all things is formed.
This is natural existence; it does not come from nothing.
Best Regards, Chian Fan
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